Page 246 - Dust Explosions in the Process Industries

2 18 Dust Explosions in the Process Industries

Figure 3.15 Particles in sample of dust fr om
Australian wheat grain. Elongated fibrous partic des
(hairs) are typical of wheat grain dusts.

If the particle shape differs appreciably from sphericity, as illustrated in Figure 3.15,
Stokes’ law for the terminal velocity of a sphere cannot be applied unless some equiva-
lent particle diameter is used, as indicated in Figure 3.13. This is often done by regard-
ing an Gbitrary particle as having a nominal “Stokes”’ diameter equal to that of a sphere
of the same density, which has the same terminal velocity as the arbitrary particle.
According to Herdan (1960), calculations have been made of the drag on ellipsoids
and infinitely long cylinders, flat blades, and infinitely thin disks. The theoretical drag
depends on the particle orientation with respect to the direction of motion. Therefore,
the viscous drag for a disk moving edge on is equal to that on a sphere with a diameter
16/9n times that of the disk, compared with 24/9z times that when the disk is moving
broadside. As a rough approximation, it has been suggested that the viscous drag on a
particle of any shape, taking an averaged orientation, is equivalent to the drag on a
sphere having the same surface area as the particle. Rumpf (1975) also discussed the influ-
ence of the particle shape on the drag acting on the particle.
The particle density may not be known in some cases, as discussed by Rudinger (1980).
One may then define an “aerodynamic” or “kinetic” diameter as the diameter of a spheri-
cal particle of density 1 g/cm3 that has the same terminal settling velocity as the particle.

3.5.3
MOVEMENT OF A PARTICLE IN AN ARBITRARY FLOW

In an arbitrary, nonsteady flow, the influence of gravity can be neglected whenever the
drag force exerted on the particle by the motion of the gas is considerably greater than
the weight of the particle. As an illustration, Rudinger (1980) discussed the case where
a particle is introduced into a gas flow of velocity

v(t) = v,+ bt (3.18)
at time t = 0. The initial velocity of the particle is 0. The constant b can be either posi-
tive or negative. Then, the velocity v,(t) of the particle at time t equals

v,(t) = v(t)-bzV+vo(bzV/~,-l)exp(-t/zv) (3.19)